1. Field of the Invention
The present invention relates to a signal processor, a signal processing method, a signal processing program, a recording medium with the signal process program recorded therein, and a measuring instrument. More specifically this invention relates to a signal processor, a signal processing method, a signal processing program each for executing the processing for filtering measurement data obtained two-dimensionally or three-dimensionally, a recording medium with the signal processing program recorded therein, and a measuring instrument.
2. Description of Related Art
There have been known various types of surface characteristics measuring instruments for measuring a contour, roughness, waviness and other properties of a surface of a workpiece for measurement such as a coordinate measuring machine for measuring a three-dimensional form of a workpiece for measurement, a contour measuring instrument or an image measuring instrument for measuring a two-dimensional contour, a roundness measuring instrument for measuring roundness, and a surface roughness measuring instrument for measuring waviness, roughness or other properties of a surface of a workpiece for measurement. These measuring instruments are used for collection of measurement data concerning a surface of a workpiece for measurement by moving a contact type sensor or a non-contact type sensor and the workpiece for measurement relatively to each other.
The measurement data collected as described above generally includes external disturbance factors such as noises.
The external disturbance factors mainly include electric/magnetic induction noises including high frequency factors, and when it is necessary to measure a contour of a surface of a workpiece for measurement, such factors as surface roughness and waviness may be the external disturbance factors.
In order to remove the external disturbance factor according to the necessity, there has been employed the method in which measurement data is converted from analog signals to digital signals and the digital signals are subjected to filtering with a filtering program for a computer. By means of this filtering processing, for instance, the high frequency factors are removed.
There has been known the Gaussian regression filter as a filter capable of executing filtering as described above (Refer to, for instance, reference 1: ISO/TR 16610-10:2000(E) Geometrical Product Specification (GPS)-Data extraction techniques by sampling and filtration-Part 10: Robust Gaussian regression filter, 1999). This filter executes the Gaussian distribution function type of weighting to measurement data yi (I=1, 2, 3, . . . ) obtained when a surface of a workpiece for measurement is measured with a prespecified sampling pitch Δx in the x-axial direction.
Assuming the Gaussian distribution function as sik, the filter output gk for the measurement data yi is expressed as follows:
                                          g            k                    =                                                    ∑                                  i                  =                  0                                                  n                  -                  1                                            ⁢                                                          ⁢                                                                    y                    i                                    ·                                      s                    ik                    ′                                                  ⁢                                                                  ⁢                k                                      =            0                          ,        1        ,        2        ,                              ⋯            ⁢                                                  ⁢            n                    -          1                                    (        1        )            
Herein the Gaussian distribution function sik is standardized and is expressed by the following expression:
                                          s            ik                    =                                                    1                                                      λ                    c                                    ⁢                                                            ln                      ⁡                                              (                        2                        )                                                                                                        ·              exp                        ⁢                          {                              -                                                                                                    π                        2                                            ·                                                                        (                                                      i                            -                            k                                                    )                                                2                                            ·                      Δ                                        ⁢                                                                                  ⁢                                          x                      2                                                                                                  ln                      ⁡                                              (                        2                        )                                                              ·                                          λ                      c                      2                                                                                  }                                      ⁢                                  ⁢                              s            ik            ′                    =                                    s              ik                                                      ∑                                  i                  =                  0                                                  n                  -                  1                                            ⁢                              s                ik                                                                        (        2        )            wherein Δx indicates a sampling pitch along the x-axis and λc indicates a cut-off wavelength.
Further there has been known the robust Gaussian regression filter having the robustness provided by adjusting a weighting factor for each measurement data according to a degree of residual error dk between the measurement data yi and the data gk having been subjected to filtration. (Refer to, for instance 1, reference 2: S. Brinkmann et al., Accessing roughness in three-dimensions using Gaussian regression filtering, International Journal of Machine Tools & Manufacture 41 (2001) 2153-2161, reference 3: S. Brinksmann et al., Development of a robust Gaussian regression filter for three-dimensional surface analysis, Xth International Colloquium on Surface, 2000, pp 122-132).
With the Gaussian regression filter and the robust Gaussian regression filter as described above, all data can be subjected to filtration without the necessity of deleting some of measurement data or adding quasi data. Especially filtration can be carried out suppressing generation of distortion at both ends of a measurement area.
Further, with the robust Gaussian regression filter, a result of filtration can be obtained without being affected by abnormal data.
In the robust Gaussian regression filter updating a weighting factor, there has been known the method in which a weighting factor is updated based on a residual error between each data value and an output value after the initial processing for filtration, and in updating a weighting factor, each data is weighted based on a median of the residual error.
However, when one median is obtained for all of measurement data and this median is applied to all of the data, local fluctuations of the data can not be grasped.
For instance, in a case of data with a very small noise level as shown in FIG. 11, a median of a residual error between initial data and filter output is very small. Therefore when a weighting factor is updated according to the median, a number of data regarded as abnormal data and having the apparent weight of zero increases. Especially, distortions are generated at both ends of the measurement area due to the initial processing, and therefore the distortions become very larger by the robust processing associated with updating of a weighting factor.
Further, in a case where there is a step-formed abrupt change in the data as shown in FIG. 12, data becomes dull by a value equivalent to the cut-off wavelength through the initial processing. Therefore, when a weight is updated according to the median, a weight of data becomes zero at a step-like changing point in the data, and as a result the filter output waveform does not reflect an accurate form of a measured surface because of the robust processing updating a weight.